When dd had a uti she was really off colour, high temperature and screamed constantly so I would think it is doubtful.
However a friend's dd at around 2, who was just toilet trained, shrieked when she weed (I remember because we were at a bday party at the time)and kept trying to hold it in instead. She had in fact scratched herself and got a small cut, like a paper cut, on her bits which would sting when she weed or probably also if sat in a bath. Could she have sat on something awkwardly or scratched herself. In friend's dd's case she plastered it with nappy cream and it healed within days.
hope she feels better soon,